On the Salient Limitations of the Methods of Assembly Theory and their Classification of Molecular Biosignatures

We demonstrate that the assembly pathway method underlying ``Assembly Theory" (AT) is a suboptimal restricted version of Huffman's encoding (Shannon-Fano type) for `counting copies,' the stated objective of the authors of AT, introduced in computer science in the 1960s and widely used by popular statistical and computable compression algorithms that have been applied to all sort of biosignatures before. We show how simple modular instructions can mislead AT, leading to failure to accomplish what the authors originally intended (counting the `number of copies') or to capture subtleties, beyond very trivial statistical properties of biological systems. We present cases whose low complexity can arbitrarily diverge from the random-like appearance to which the AT would assign arbitrarily high statistical significance, and show that it fails in simple cases (synthetic or natural) which the assembly theory was supposed to shed some light on. Our theoretical and empirical results imply that the assembly index, whose computable nature is not an advantage, does not offer any substantial improvement over existing concepts and methods, computable or (semi) uncomputable. No strong compression or algorithmic complexity results were required to prove that AT and MA are ill-defined and under-perform as compared to simple coding schemes. We show that despite the claims of experimental data, the assembly measure is driven mostly or only by InChI codes which had already been reported before to discriminate organic from inorganic compounds by other indexes.